Hierarchical MPC for coupled subsystems using adjustable tubes

TL;DR

This paper introduces a hierarchical MPC framework for coupled linear systems that uses adjustable tubes represented as zonotopes to reduce computational complexity while ensuring constraint satisfaction.

Contribution

It proposes a novel hierarchical control scheme with adjustable tubes for coupled systems, optimizing uncertainty bounds and constraint tightening online.

Findings

Reduces computational cost compared to centralized MPC.

Ensures state and input constraint satisfaction.

Demonstrates effectiveness through a numerical example.

Abstract

A hierarchical Model Predictive Control (MPC) formulation is presented for coupled discrete-time linear systems with state and input constraints. Compared to a centralized approach, a two-level hierarchical controller, with one controller in the upper-level and one controller per subsystem in the lower-level, can significantly reduce the computational cost associated with MPC. Hierarchical coordination is achieved using adjustable tubes, which are optimized by the upper-level controller and bound permissible lower-level controller deviations from the system trajectories determined by the upper-level controller. The size of these adjustable tubes determines the degree of uncertainty between subsystems and directly affects the required constraint tightening under a tube-based robust MPC framework. Sets are represented as zonotopes to enable the ability to optimize the size of these adjustable tubes and perform the necessary constraint tightening online as part of the MPC optimization problems. State and input constraint satisfaction is proven for the two-level hierarchical controller with an arbitrary number of controllers at the lower-level and a numerical example demonstrates the key features and performance of the approach.